Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2025,2,Mod(649,2025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2025.649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2025 = 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2025.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.1697064093\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 405) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.3 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2025.649 |
Dual form | 2025.2.b.g.649.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2025\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(1702\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.732051i | 0.517638i | 0.965926 | + | 0.258819i | \(0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.46410 | 0.732051 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 4.73205i | − 1.78855i | −0.447521 | − | 0.894274i | \(-0.647693\pi\) | ||||
0.447521 | − | 0.894274i | \(-0.352307\pi\) | |||||||
\(8\) | 2.53590i | 0.896575i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.73205 | −1.72828 | −0.864139 | − | 0.503253i | \(-0.832136\pi\) | ||||
−0.864139 | + | 0.503253i | \(0.832136\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.46410i | − 0.406069i | −0.979172 | − | 0.203034i | \(-0.934920\pi\) | ||||
0.979172 | − | 0.203034i | \(-0.0650803\pi\) | |||||||
\(14\) | 3.46410 | 0.925820 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.07180 | 0.267949 | ||||||||
\(17\) | − 2.73205i | − 0.662620i | −0.943522 | − | 0.331310i | \(-0.892509\pi\) | ||||
0.943522 | − | 0.331310i | \(-0.107491\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.46410 | −1.02414 | −0.512068 | − | 0.858945i | \(-0.671120\pi\) | ||||
−0.512068 | + | 0.858945i | \(0.671120\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 4.19615i | − 0.894623i | ||||||||
\(23\) | 3.46410i | 0.722315i | 0.932505 | + | 0.361158i | \(0.117618\pi\) | ||||
−0.932505 | + | 0.361158i | \(0.882382\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.07180 | 0.210197 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 6.92820i | − 1.30931i | ||||||||
\(29\) | −3.19615 | −0.593511 | −0.296755 | − | 0.954954i | \(-0.595905\pi\) | ||||
−0.296755 | + | 0.954954i | \(0.595905\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | −0.538816 | −0.269408 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269408 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(32\) | 5.85641i | 1.03528i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.73205i | − 0.449146i | −0.974457 | − | 0.224573i | \(-0.927901\pi\) | ||||
0.974457 | − | 0.224573i | \(-0.0720988\pi\) | |||||||
\(38\) | − 3.26795i | − 0.530131i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.19615 | −1.12385 | −0.561925 | − | 0.827188i | \(-0.689939\pi\) | ||||
−0.561925 | + | 0.827188i | \(0.689939\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 0.196152i | − 0.0299130i | −0.999888 | − | 0.0149565i | \(-0.995239\pi\) | ||||
0.999888 | − | 0.0149565i | \(-0.00476097\pi\) | |||||||
\(44\) | −8.39230 | −1.26519 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.53590 | −0.373898 | ||||||||
\(47\) | − 8.73205i | − 1.27370i | −0.770988 | − | 0.636850i | \(-0.780237\pi\) | ||||
0.770988 | − | 0.636850i | \(-0.219763\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.3923 | −2.19890 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 2.14359i | − 0.297263i | ||||||||
\(53\) | − 6.73205i | − 0.924718i | −0.886693 | − | 0.462359i | \(-0.847003\pi\) | ||||
0.886693 | − | 0.462359i | \(-0.152997\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12.0000 | 1.60357 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 2.33975i | − 0.307224i | ||||||||
\(59\) | 8.26795 | 1.07640 | 0.538198 | − | 0.842819i | \(-0.319105\pi\) | ||||
0.538198 | + | 0.842819i | \(0.319105\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.00000 | 0.512148 | 0.256074 | − | 0.966657i | \(-0.417571\pi\) | ||||
0.256074 | + | 0.966657i | \(0.417571\pi\) | |||||||
\(62\) | − 2.19615i | − 0.278912i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.14359 | −0.267949 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.46410i | 0.423207i | 0.977356 | + | 0.211604i | \(0.0678686\pi\) | ||||
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | − 4.00000i | − 0.485071i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.73205 | −0.442913 | −0.221456 | − | 0.975170i | \(-0.571081\pi\) | ||||
−0.221456 | + | 0.975170i | \(0.571081\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.66025i | 0.896565i | 0.893892 | + | 0.448282i | \(0.147964\pi\) | ||||
−0.893892 | + | 0.448282i | \(0.852036\pi\) | |||||||
\(74\) | 2.00000 | 0.232495 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.53590 | −0.749719 | ||||||||
\(77\) | 27.1244i | 3.09111i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.4641 | −1.73985 | −0.869924 | − | 0.493186i | \(-0.835832\pi\) | ||||
−0.869924 | + | 0.493186i | \(0.835832\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 5.26795i | − 0.581748i | ||||||||
\(83\) | − 2.19615i | − 0.241059i | −0.992710 | − | 0.120530i | \(-0.961541\pi\) | ||||
0.992710 | − | 0.120530i | \(-0.0384592\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.143594 | 0.0154841 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 14.5359i | − 1.54953i | ||||||||
\(89\) | −5.19615 | −0.550791 | −0.275396 | − | 0.961331i | \(-0.588809\pi\) | ||||
−0.275396 | + | 0.961331i | \(0.588809\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.92820 | −0.726273 | ||||||||
\(92\) | 5.07180i | 0.528771i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.39230 | 0.659316 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 9.66025i | − 0.980850i | −0.871483 | − | 0.490425i | \(-0.836842\pi\) | ||||
0.871483 | − | 0.490425i | \(-0.163158\pi\) | |||||||
\(98\) | − 11.2679i | − 1.13823i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.66025 | −0.264705 | −0.132353 | − | 0.991203i | \(-0.542253\pi\) | ||||
−0.132353 | + | 0.991203i | \(0.542253\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.535898i | 0.0528036i | 0.999651 | + | 0.0264018i | \(0.00840494\pi\) | ||||
−0.999651 | + | 0.0264018i | \(0.991595\pi\) | |||||||
\(104\) | 3.71281 | 0.364071 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.92820 | 0.478669 | ||||||||
\(107\) | − 8.53590i | − 0.825196i | −0.910913 | − | 0.412598i | \(-0.864621\pi\) | ||||
0.910913 | − | 0.412598i | \(-0.135379\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.07180 | 0.581573 | 0.290786 | − | 0.956788i | \(-0.406083\pi\) | ||||
0.290786 | + | 0.956788i | \(0.406083\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 5.07180i | − 0.479240i | ||||||||
\(113\) | 19.1244i | 1.79907i | 0.436851 | + | 0.899534i | \(0.356094\pi\) | ||||
−0.436851 | + | 0.899534i | \(0.643906\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.67949 | −0.434480 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.05256i | 0.557183i | ||||||||
\(119\) | −12.9282 | −1.18513 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.8564 | 1.98695 | ||||||||
\(122\) | 2.92820i | 0.265107i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.39230 | −0.394441 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 14.5885i | − 1.29452i | −0.762271 | − | 0.647258i | \(-0.775916\pi\) | ||||
0.762271 | − | 0.647258i | \(-0.224084\pi\) | |||||||
\(128\) | 10.1436i | 0.896575i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.5885 | 1.36197 | 0.680985 | − | 0.732297i | \(-0.261552\pi\) | ||||
0.680985 | + | 0.732297i | \(0.261552\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 21.1244i | 1.83171i | ||||||||
\(134\) | −2.53590 | −0.219068 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.92820 | 0.594089 | ||||||||
\(137\) | 2.53590i | 0.216656i | 0.994115 | + | 0.108328i | \(0.0345497\pi\) | ||||
−0.994115 | + | 0.108328i | \(0.965450\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.607695 | −0.0515440 | −0.0257720 | − | 0.999668i | \(-0.508204\pi\) | ||||
−0.0257720 | + | 0.999668i | \(0.508204\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 2.73205i | − 0.229269i | ||||||||
\(143\) | 8.39230i | 0.701800i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.60770 | −0.464096 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 4.00000i | − 0.328798i | ||||||||
\(149\) | 8.00000 | 0.655386 | 0.327693 | − | 0.944784i | \(-0.393729\pi\) | ||||
0.327693 | + | 0.944784i | \(0.393729\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.39230 | 0.438820 | 0.219410 | − | 0.975633i | \(-0.429587\pi\) | ||||
0.219410 | + | 0.975633i | \(0.429587\pi\) | |||||||
\(152\) | − 11.3205i | − 0.918214i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −19.8564 | −1.60007 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 19.1244i | − 1.52629i | −0.646227 | − | 0.763145i | \(-0.723654\pi\) | ||||
0.646227 | − | 0.763145i | \(-0.276346\pi\) | |||||||
\(158\) | − 11.3205i | − 0.900611i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.3923 | 1.29189 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 12.7321i | − 0.997251i | −0.866817 | − | 0.498626i | \(-0.833838\pi\) | ||||
0.866817 | − | 0.498626i | \(-0.166162\pi\) | |||||||
\(164\) | −10.5359 | −0.822715 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.60770 | 0.124781 | ||||||||
\(167\) | − 17.6603i | − 1.36659i | −0.730142 | − | 0.683296i | \(-0.760546\pi\) | ||||
0.730142 | − | 0.683296i | \(-0.239454\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.8564 | 0.835108 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 0.287187i | − 0.0218978i | ||||||||
\(173\) | − 8.53590i | − 0.648972i | −0.945890 | − | 0.324486i | \(-0.894809\pi\) | ||||
0.945890 | − | 0.324486i | \(-0.105191\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.14359 | −0.463091 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 3.80385i | − 0.285110i | ||||||||
\(179\) | −8.12436 | −0.607243 | −0.303621 | − | 0.952793i | \(-0.598196\pi\) | ||||
−0.303621 | + | 0.952793i | \(0.598196\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 26.4641 | 1.96706 | 0.983531 | − | 0.180742i | \(-0.0578498\pi\) | ||||
0.983531 | + | 0.180742i | \(0.0578498\pi\) | |||||||
\(182\) | − 5.07180i | − 0.375947i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.78461 | −0.647610 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.6603i | 1.14519i | ||||||||
\(188\) | − 12.7846i | − 0.932413i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.12436 | −0.587858 | −0.293929 | − | 0.955827i | \(-0.594963\pi\) | ||||
−0.293929 | + | 0.955827i | \(0.594963\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.26795i | 0.379195i | 0.981862 | + | 0.189598i | \(0.0607184\pi\) | ||||
−0.981862 | + | 0.189598i | \(0.939282\pi\) | |||||||
\(194\) | 7.07180 | 0.507725 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −22.5359 | −1.60971 | ||||||||
\(197\) | − 13.8564i | − 0.987228i | −0.869681 | − | 0.493614i | \(-0.835676\pi\) | ||||
0.869681 | − | 0.493614i | \(-0.164324\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000 | 0.141776 | 0.0708881 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708881 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 1.94744i | − 0.137021i | ||||||||
\(203\) | 15.1244i | 1.06152i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.392305 | −0.0273332 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 1.56922i | − 0.108806i | ||||||||
\(209\) | 25.5885 | 1.76999 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.85641 | −0.609700 | −0.304850 | − | 0.952400i | \(-0.598606\pi\) | ||||
−0.304850 | + | 0.952400i | \(0.598606\pi\) | |||||||
\(212\) | − 9.85641i | − 0.676941i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.24871 | 0.427153 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.1962i | 0.963698i | ||||||||
\(218\) | 4.44486i | 0.301044i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 16.7846i | − 1.12398i | −0.827144 | − | 0.561990i | \(-0.810036\pi\) | ||||
0.827144 | − | 0.561990i | \(-0.189964\pi\) | |||||||
\(224\) | 27.7128 | 1.85164 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.0000 | −0.931266 | ||||||||
\(227\) | − 18.0526i | − 1.19819i | −0.800678 | − | 0.599095i | \(-0.795527\pi\) | ||||
0.800678 | − | 0.599095i | \(-0.204473\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.0000 | 0.792982 | 0.396491 | − | 0.918039i | \(-0.370228\pi\) | ||||
0.396491 | + | 0.918039i | \(0.370228\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 8.10512i | − 0.532127i | ||||||||
\(233\) | 28.0526i | 1.83778i | 0.394509 | + | 0.918892i | \(0.370915\pi\) | ||||
−0.394509 | + | 0.918892i | \(0.629085\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.1051 | 0.787976 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 9.46410i | − 0.613467i | ||||||||
\(239\) | 0.535898 | 0.0346644 | 0.0173322 | − | 0.999850i | \(-0.494483\pi\) | ||||
0.0173322 | + | 0.999850i | \(0.494483\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.3205 | −1.05130 | −0.525648 | − | 0.850702i | \(-0.676177\pi\) | ||||
−0.525648 | + | 0.850702i | \(0.676177\pi\) | |||||||
\(242\) | 16.0000i | 1.02852i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.85641 | 0.374918 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.53590i | 0.415869i | ||||||||
\(248\) | − 7.60770i | − 0.483089i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.3923 | −0.655956 | −0.327978 | − | 0.944685i | \(-0.606367\pi\) | ||||
−0.327978 | + | 0.944685i | \(0.606367\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 19.8564i | − 1.24836i | ||||||||
\(254\) | 10.6795 | 0.670091 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.7128 | −0.732051 | ||||||||
\(257\) | 10.3923i | 0.648254i | 0.946014 | + | 0.324127i | \(0.105071\pi\) | ||||
−0.946014 | + | 0.324127i | \(0.894929\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −12.9282 | −0.803319 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.4115i | 0.705007i | ||||||||
\(263\) | − 21.3205i | − 1.31468i | −0.753595 | − | 0.657339i | \(-0.771682\pi\) | ||||
0.753595 | − | 0.657339i | \(-0.228318\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −15.4641 | −0.948165 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.07180i | 0.309809i | ||||||||
\(269\) | −10.6603 | −0.649967 | −0.324984 | − | 0.945720i | \(-0.605359\pi\) | ||||
−0.324984 | + | 0.945720i | \(0.605359\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.92820 | −0.177876 | −0.0889378 | − | 0.996037i | \(-0.528347\pi\) | ||||
−0.0889378 | + | 0.996037i | \(0.528347\pi\) | |||||||
\(272\) | − 2.92820i | − 0.177548i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.85641 | −0.112150 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.80385i | 0.228551i | 0.993449 | + | 0.114276i | \(0.0364547\pi\) | ||||
−0.993449 | + | 0.114276i | \(0.963545\pi\) | |||||||
\(278\) | − 0.444864i | − 0.0266812i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.4641 | 0.922511 | 0.461255 | − | 0.887267i | \(-0.347399\pi\) | ||||
0.461255 | + | 0.887267i | \(0.347399\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.3205i | 1.74292i | 0.490464 | + | 0.871462i | \(0.336827\pi\) | ||||
−0.490464 | + | 0.871462i | \(0.663173\pi\) | |||||||
\(284\) | −5.46410 | −0.324235 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.14359 | −0.363278 | ||||||||
\(287\) | 34.0526i | 2.01006i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.53590 | 0.560935 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.2154i | 0.656331i | ||||||||
\(293\) | − 28.7321i | − 1.67854i | −0.543712 | − | 0.839272i | \(-0.682981\pi\) | ||||
0.543712 | − | 0.839272i | \(-0.317019\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6.92820 | 0.402694 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.85641i | 0.339253i | ||||||||
\(299\) | 5.07180 | 0.293310 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.928203 | −0.0535007 | ||||||||
\(302\) | 3.94744i | 0.227150i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.78461 | −0.274416 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.0526i | 0.802022i | 0.916073 | + | 0.401011i | \(0.131341\pi\) | ||||
−0.916073 | + | 0.401011i | \(0.868659\pi\) | |||||||
\(308\) | 39.7128i | 2.26285i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.7321 | 1.11890 | 0.559451 | − | 0.828863i | \(-0.311012\pi\) | ||||
0.559451 | + | 0.828863i | \(0.311012\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.07180i | 0.512768i | 0.966575 | + | 0.256384i | \(0.0825312\pi\) | ||||
−0.966575 | + | 0.256384i | \(0.917469\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −22.6410 | −1.27366 | ||||||||
\(317\) | 6.19615i | 0.348011i | 0.984745 | + | 0.174005i | \(0.0556710\pi\) | ||||
−0.984745 | + | 0.174005i | \(0.944329\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.3205 | 1.02575 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.0000i | 0.668734i | ||||||||
\(323\) | 12.1962i | 0.678612i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.32051 | 0.516215 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 18.2487i | − 1.00762i | ||||||||
\(329\) | −41.3205 | −2.27807 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.464102 | −0.0255093 | −0.0127547 | − | 0.999919i | \(-0.504060\pi\) | ||||
−0.0127547 | + | 0.999919i | \(0.504060\pi\) | |||||||
\(332\) | − 3.21539i | − 0.176467i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.9282 | 0.707400 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.3205i | 1.48824i | 0.668044 | + | 0.744121i | \(0.267132\pi\) | ||||
−0.668044 | + | 0.744121i | \(0.732868\pi\) | |||||||
\(338\) | 7.94744i | 0.432284i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.1962 | 0.931224 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 39.7128i | 2.14429i | ||||||||
\(344\) | 0.497423 | 0.0268192 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.24871 | 0.335933 | ||||||||
\(347\) | − 28.5885i | − 1.53471i | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
0.641223 | − | 0.767354i | \(-0.278427\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.8564 | 1.00936 | 0.504680 | − | 0.863306i | \(-0.331610\pi\) | ||||
0.504680 | + | 0.863306i | \(0.331610\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 33.5692i | − 1.78925i | ||||||||
\(353\) | − 25.5167i | − 1.35811i | −0.734085 | − | 0.679057i | \(-0.762389\pi\) | ||||
0.734085 | − | 0.679057i | \(-0.237611\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.60770 | −0.403207 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 5.94744i | − 0.314332i | ||||||||
\(359\) | 6.12436 | 0.323231 | 0.161616 | − | 0.986854i | \(-0.448330\pi\) | ||||
0.161616 | + | 0.986854i | \(0.448330\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.928203 | 0.0488528 | ||||||||
\(362\) | 19.3731i | 1.01823i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.1436 | −0.531669 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.1769i | 1.62742i | 0.581270 | + | 0.813711i | \(0.302556\pi\) | ||||
−0.581270 | + | 0.813711i | \(0.697444\pi\) | |||||||
\(368\) | 3.71281i | 0.193544i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −31.8564 | −1.65390 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 20.0526i | − 1.03828i | −0.854689 | − | 0.519141i | \(-0.826252\pi\) | ||||
0.854689 | − | 0.519141i | \(-0.173748\pi\) | |||||||
\(374\) | −11.4641 | −0.592795 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 22.1436 | 1.14197 | ||||||||
\(377\) | 4.67949i | 0.241006i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.39230 | −0.122884 | −0.0614422 | − | 0.998111i | \(-0.519570\pi\) | ||||
−0.0614422 | + | 0.998111i | \(0.519570\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 5.94744i | − 0.304298i | ||||||||
\(383\) | − 2.53590i | − 0.129578i | −0.997899 | − | 0.0647892i | \(-0.979363\pi\) | ||||
0.997899 | − | 0.0647892i | \(-0.0206375\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.85641 | −0.196286 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 14.1436i | − 0.718032i | ||||||||
\(389\) | −27.4641 | −1.39249 | −0.696243 | − | 0.717807i | \(-0.745146\pi\) | ||||
−0.696243 | + | 0.717807i | \(0.745146\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.46410 | 0.478620 | ||||||||
\(392\) | − 39.0333i | − 1.97148i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.1436 | 0.511027 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.3923i | 0.722329i | 0.932502 | + | 0.361165i | \(0.117621\pi\) | ||||
−0.932502 | + | 0.361165i | \(0.882379\pi\) | |||||||
\(398\) | 1.46410i | 0.0733888i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.9282 | 1.24486 | 0.622428 | − | 0.782677i | \(-0.286147\pi\) | ||||
0.622428 | + | 0.782677i | \(0.286147\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.39230i | 0.218796i | ||||||||
\(404\) | −3.89488 | −0.193778 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.0718 | −0.549484 | ||||||||
\(407\) | 15.6603i | 0.776250i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.8564 | 0.882942 | 0.441471 | − | 0.897275i | \(-0.354457\pi\) | ||||
0.441471 | + | 0.897275i | \(0.354457\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.784610i | 0.0386549i | ||||||||
\(413\) | − 39.1244i | − 1.92518i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 8.57437 | 0.420393 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.7321i | 0.916215i | ||||||||
\(419\) | −20.3923 | −0.996229 | −0.498115 | − | 0.867111i | \(-0.665974\pi\) | ||||
−0.498115 | + | 0.867111i | \(0.665974\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.7846 | 1.64656 | 0.823281 | − | 0.567635i | \(-0.192141\pi\) | ||||
0.823281 | + | 0.567635i | \(0.192141\pi\) | |||||||
\(422\) | − 6.48334i | − 0.315604i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 17.0718 | 0.829080 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 18.9282i | − 0.916000i | ||||||||
\(428\) | − 12.4974i | − 0.604086i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.3397 | −1.02790 | −0.513950 | − | 0.857820i | \(-0.671818\pi\) | ||||
−0.513950 | + | 0.857820i | \(0.671818\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.4641i | 1.70430i | 0.523301 | + | 0.852148i | \(0.324700\pi\) | ||||
−0.523301 | + | 0.852148i | \(0.675300\pi\) | |||||||
\(434\) | −10.3923 | −0.498847 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.88973 | 0.425741 | ||||||||
\(437\) | − 15.4641i | − 0.739748i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.39230 | −0.257361 | −0.128680 | − | 0.991686i | \(-0.541074\pi\) | ||||
−0.128680 | + | 0.991686i | \(0.541074\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 2.92820i | − 0.139280i | ||||||||
\(443\) | 0.339746i | 0.0161418i | 0.999967 | + | 0.00807091i | \(0.00256908\pi\) | ||||
−0.999967 | + | 0.00807091i | \(0.997431\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 12.2872 | 0.581815 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10.1436i | 0.479240i | ||||||||
\(449\) | −8.12436 | −0.383412 | −0.191706 | − | 0.981452i | \(-0.561402\pi\) | ||||
−0.191706 | + | 0.981452i | \(0.561402\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 41.2487 | 1.94233 | ||||||||
\(452\) | 28.0000i | 1.31701i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.2154 | 0.620229 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.73205i | 0.127800i | 0.997956 | + | 0.0639000i | \(0.0203539\pi\) | ||||
−0.997956 | + | 0.0639000i | \(0.979646\pi\) | |||||||
\(458\) | 8.78461i | 0.410478i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.0526 | −1.72571 | −0.862855 | − | 0.505452i | \(-0.831326\pi\) | ||||
−0.862855 | + | 0.505452i | \(0.831326\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.3923i | 0.482971i | 0.970404 | + | 0.241486i | \(0.0776347\pi\) | ||||
−0.970404 | + | 0.241486i | \(0.922365\pi\) | |||||||
\(464\) | −3.42563 | −0.159031 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.5359 | −0.951307 | ||||||||
\(467\) | 37.3731i | 1.72942i | 0.502272 | + | 0.864710i | \(0.332498\pi\) | ||||
−0.502272 | + | 0.864710i | \(0.667502\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.3923 | 0.756926 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 20.9667i | 0.965070i | ||||||||
\(473\) | 1.12436i | 0.0516979i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −18.9282 | −0.867573 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.392305i | 0.0179436i | ||||||||
\(479\) | 11.8756 | 0.542612 | 0.271306 | − | 0.962493i | \(-0.412544\pi\) | ||||
0.271306 | + | 0.962493i | \(0.412544\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.00000 | −0.182384 | ||||||||
\(482\) | − 11.9474i | − 0.544191i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 32.0000 | 1.45455 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.3923i | 1.10532i | 0.833407 | + | 0.552660i | \(0.186387\pi\) | ||||
−0.833407 | + | 0.552660i | \(0.813613\pi\) | |||||||
\(488\) | 10.1436i | 0.459179i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.8756 | −0.626199 | −0.313100 | − | 0.949720i | \(-0.601367\pi\) | ||||
−0.313100 | + | 0.949720i | \(0.601367\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.73205i | 0.393272i | ||||||||
\(494\) | −4.78461 | −0.215270 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.21539 | −0.144375 | ||||||||
\(497\) | 17.6603i | 0.792171i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.3205 | −1.08874 | −0.544368 | − | 0.838847i | \(-0.683230\pi\) | ||||
−0.544368 | + | 0.838847i | \(0.683230\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 7.60770i | − 0.339548i | ||||||||
\(503\) | 7.32051i | 0.326405i | 0.986593 | + | 0.163203i | \(0.0521824\pi\) | ||||
−0.986593 | + | 0.163203i | \(0.947818\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 14.5359 | 0.646200 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 21.3590i | − 0.947652i | ||||||||
\(509\) | 6.78461 | 0.300723 | 0.150361 | − | 0.988631i | \(-0.451956\pi\) | ||||
0.150361 | + | 0.988631i | \(0.451956\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.2487 | 1.60355 | ||||||||
\(512\) | 11.7128i | 0.517638i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.60770 | −0.335561 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 50.0526i | 2.20131i | ||||||||
\(518\) | − 9.46410i | − 0.415829i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.4641 | 0.852738 | 0.426369 | − | 0.904549i | \(-0.359793\pi\) | ||||
0.426369 | + | 0.904549i | \(0.359793\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 22.2487i | − 0.972868i | −0.873717 | − | 0.486434i | \(-0.838297\pi\) | ||||
0.873717 | − | 0.486434i | \(-0.161703\pi\) | |||||||
\(524\) | 22.8231 | 0.997031 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.6077 | 0.680528 | ||||||||
\(527\) | 8.19615i | 0.357030i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | 0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 30.9282i | 1.34091i | ||||||||
\(533\) | 10.5359i | 0.456360i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −8.78461 | −0.379437 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 7.80385i | − 0.336448i | ||||||||
\(539\) | 88.2295 | 3.80031 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.4641 | −1.05179 | −0.525897 | − | 0.850548i | \(-0.676270\pi\) | ||||
−0.525897 | + | 0.850548i | \(0.676270\pi\) | |||||||
\(542\) | − 2.14359i | − 0.0920752i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 16.0000 | 0.685994 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 33.8564i | − 1.44760i | −0.690012 | − | 0.723798i | \(-0.742395\pi\) | ||||
0.690012 | − | 0.723798i | \(-0.257605\pi\) | |||||||
\(548\) | 3.71281i | 0.158604i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.2679 | 0.607835 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 73.1769i | 3.11180i | ||||||||
\(554\) | −2.78461 | −0.118307 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.889727 | −0.0377328 | ||||||||
\(557\) | − 2.53590i | − 0.107449i | −0.998556 | − | 0.0537247i | \(-0.982891\pi\) | ||||
0.998556 | − | 0.0537247i | \(-0.0171094\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.287187 | −0.0121467 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 11.3205i | 0.477527i | ||||||||
\(563\) | 16.7321i | 0.705172i | 0.935779 | + | 0.352586i | \(0.114698\pi\) | ||||
−0.935779 | + | 0.352586i | \(0.885302\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −21.4641 | −0.902203 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 9.46410i | − 0.397105i | ||||||||
\(569\) | 32.9090 | 1.37962 | 0.689808 | − | 0.723993i | \(-0.257695\pi\) | ||||
0.689808 | + | 0.723993i | \(0.257695\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.7846 | −1.66493 | −0.832467 | − | 0.554075i | \(-0.813072\pi\) | ||||
−0.832467 | + | 0.554075i | \(0.813072\pi\) | |||||||
\(572\) | 12.2872i | 0.513753i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −24.9282 | −1.04048 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.2679i | 0.635613i | 0.948156 | + | 0.317807i | \(0.102946\pi\) | ||||
−0.948156 | + | 0.317807i | \(0.897054\pi\) | |||||||
\(578\) | 6.98076i | 0.290361i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.3923 | −0.431145 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.5885i | 1.59817i | ||||||||
\(584\) | −19.4256 | −0.803838 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.0333 | 0.868878 | ||||||||
\(587\) | − 11.6603i | − 0.481270i | −0.970616 | − | 0.240635i | \(-0.922644\pi\) | ||||
0.970616 | − | 0.240635i | \(-0.0773557\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.3923 | 0.551820 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 2.92820i | − 0.120348i | ||||||||
\(593\) | 0.143594i | 0.00589668i | 0.999996 | + | 0.00294834i | \(0.000938487\pi\) | ||||
−0.999996 | + | 0.00294834i | \(0.999062\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.7128 | 0.479776 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.71281i | 0.151828i | ||||||||
\(599\) | −27.1962 | −1.11120 | −0.555602 | − | 0.831448i | \(-0.687512\pi\) | ||||
−0.555602 | + | 0.831448i | \(0.687512\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.2487 | −1.27466 | −0.637331 | − | 0.770590i | \(-0.719961\pi\) | ||||
−0.637331 | + | 0.770590i | \(0.719961\pi\) | |||||||
\(602\) | − 0.679492i | − 0.0276940i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.89488 | 0.321238 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 16.1962i | − 0.657382i | −0.944438 | − | 0.328691i | \(-0.893393\pi\) | ||||
0.944438 | − | 0.328691i | \(-0.106607\pi\) | |||||||
\(608\) | − 26.1436i | − 1.06026i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.7846 | −0.517210 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1.46410i | − 0.0591345i | −0.999563 | − | 0.0295673i | \(-0.990587\pi\) | ||||
0.999563 | − | 0.0295673i | \(-0.00941292\pi\) | |||||||
\(614\) | −10.2872 | −0.415157 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −68.7846 | −2.77141 | ||||||||
\(617\) | − 6.92820i | − 0.278919i | −0.990228 | − | 0.139459i | \(-0.955464\pi\) | ||||
0.990228 | − | 0.139459i | \(-0.0445365\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.8564 | 0.476549 | 0.238275 | − | 0.971198i | \(-0.423418\pi\) | ||||
0.238275 | + | 0.971198i | \(0.423418\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.4449i | 0.579186i | ||||||||
\(623\) | 24.5885i | 0.985116i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.64102 | −0.265428 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 28.0000i | − 1.11732i | ||||||||
\(629\) | −7.46410 | −0.297613 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.7128 | −1.30228 | −0.651138 | − | 0.758959i | \(-0.725708\pi\) | ||||
−0.651138 | + | 0.758959i | \(0.725708\pi\) | |||||||
\(632\) | − 39.2154i | − 1.55990i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.53590 | −0.180144 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.5359i | 0.892905i | ||||||||
\(638\) | 13.4115i | 0.530968i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.33975 | 0.368898 | 0.184449 | − | 0.982842i | \(-0.440950\pi\) | ||||
0.184449 | + | 0.982842i | \(0.440950\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 41.6603i | − 1.64292i | −0.570266 | − | 0.821460i | \(-0.693160\pi\) | ||||
0.570266 | − | 0.821460i | \(-0.306840\pi\) | |||||||
\(644\) | 24.0000 | 0.945732 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.92820 | −0.351275 | ||||||||
\(647\) | 11.4641i | 0.450700i | 0.974278 | + | 0.225350i | \(0.0723526\pi\) | ||||
−0.974278 | + | 0.225350i | \(0.927647\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −47.3923 | −1.86031 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 18.6410i | − 0.730039i | ||||||||
\(653\) | 17.4641i | 0.683423i | 0.939805 | + | 0.341712i | \(0.111007\pi\) | ||||
−0.939805 | + | 0.341712i | \(0.888993\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.71281 | −0.301135 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 30.2487i | − 1.17922i | ||||||||
\(659\) | 1.46410 | 0.0570333 | 0.0285167 | − | 0.999593i | \(-0.490922\pi\) | ||||
0.0285167 | + | 0.999593i | \(0.490922\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.3205 | 0.712585 | 0.356293 | − | 0.934374i | \(-0.384041\pi\) | ||||
0.356293 | + | 0.934374i | \(0.384041\pi\) | |||||||
\(662\) | − 0.339746i | − 0.0132046i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.56922 | 0.216128 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 11.0718i | − 0.428702i | ||||||||
\(668\) | − 25.8564i | − 1.00041i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.9282 | −0.885133 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.3923i | 0.400594i | 0.979735 | + | 0.200297i | \(0.0641907\pi\) | ||||
−0.979735 | + | 0.200297i | \(0.935809\pi\) | |||||||
\(674\) | −20.0000 | −0.770371 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 15.8949 | 0.611342 | ||||||||
\(677\) | − 18.0000i | − 0.691796i | −0.938272 | − | 0.345898i | \(-0.887574\pi\) | ||||
0.938272 | − | 0.345898i | \(-0.112426\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −45.7128 | −1.75430 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.5885i | 0.482037i | ||||||||
\(683\) | 19.6077i | 0.750268i | 0.926971 | + | 0.375134i | \(0.122403\pi\) | ||||
−0.926971 | + | 0.375134i | \(0.877597\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −29.0718 | −1.10997 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 0.210236i | − 0.00801515i | ||||||||
\(689\) | −9.85641 | −0.375499 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.7128 | −0.673827 | −0.336914 | − | 0.941536i | \(-0.609383\pi\) | ||||
−0.336914 | + | 0.941536i | \(0.609383\pi\) | |||||||
\(692\) | − 12.4974i | − 0.475081i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 20.9282 | 0.794424 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.6603i | 0.744685i | ||||||||
\(698\) | 13.8038i | 0.522483i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.8038 | −0.785750 | −0.392875 | − | 0.919592i | \(-0.628520\pi\) | ||||
−0.392875 | + | 0.919592i | \(0.628520\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.1962i | 0.459987i | ||||||||
\(704\) | 12.2872 | 0.463091 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.6795 | 0.703012 | ||||||||
\(707\) | 12.5885i | 0.473438i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.5359 | 0.846353 | 0.423177 | − | 0.906047i | \(-0.360915\pi\) | ||||
0.423177 | + | 0.906047i | \(0.360915\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 13.1769i | − 0.493826i | ||||||||
\(713\) | − 10.3923i | − 0.389195i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −11.8949 | −0.444533 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.48334i | 0.167317i | ||||||||
\(719\) | −8.41154 | −0.313698 | −0.156849 | − | 0.987623i | \(-0.550134\pi\) | ||||
−0.156849 | + | 0.987623i | \(0.550134\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.53590 | 0.0944418 | ||||||||
\(722\) | 0.679492i | 0.0252881i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 38.7461 | 1.43999 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 8.39230i | − 0.311253i | −0.987816 | − | 0.155627i | \(-0.950260\pi\) | ||||
0.987816 | − | 0.155627i | \(-0.0497397\pi\) | |||||||
\(728\) | − 17.5692i | − 0.651159i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.535898 | −0.0198209 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 34.7846i | − 1.28480i | −0.766370 | − | 0.642399i | \(-0.777939\pi\) | ||||
0.766370 | − | 0.642399i | \(-0.222061\pi\) | |||||||
\(734\) | −22.8231 | −0.842415 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −20.2872 | −0.747796 | ||||||||
\(737\) | − 19.8564i | − 0.731420i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.4641 | −0.826355 | −0.413178 | − | 0.910650i | \(-0.635581\pi\) | ||||
−0.413178 | + | 0.910650i | \(0.635581\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 23.3205i | − 0.856123i | ||||||||
\(743\) | − 19.9090i | − 0.730389i | −0.930931 | − | 0.365195i | \(-0.881002\pi\) | ||||
0.930931 | − | 0.365195i | \(-0.118998\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 14.6795 | 0.537454 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 22.9282i | 0.838338i | ||||||||
\(749\) | −40.3923 | −1.47590 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.7846 | 1.78018 | 0.890088 | − | 0.455789i | \(-0.150643\pi\) | ||||
0.890088 | + | 0.455789i | \(0.150643\pi\) | |||||||
\(752\) | − 9.35898i | − 0.341287i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.42563 | −0.124754 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 9.17691i | − 0.333541i | −0.985996 | − | 0.166770i | \(-0.946666\pi\) | ||||
0.985996 | − | 0.166770i | \(-0.0533338\pi\) | |||||||
\(758\) | − 1.75129i | − 0.0636097i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.4449 | 0.849876 | 0.424938 | − | 0.905223i | \(-0.360296\pi\) | ||||
0.424938 | + | 0.905223i | \(0.360296\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 28.7321i | − 1.04017i | ||||||||
\(764\) | −11.8949 | −0.430342 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.85641 | 0.0670747 | ||||||||
\(767\) | − 12.1051i | − 0.437090i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.53590 | 0.343873 | 0.171937 | − | 0.985108i | \(-0.444998\pi\) | ||||
0.171937 | + | 0.985108i | \(0.444998\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.71281i | 0.277590i | ||||||||
\(773\) | − 1.51666i | − 0.0545505i | −0.999628 | − | 0.0272752i | \(-0.991317\pi\) | ||||
0.999628 | − | 0.0272752i | \(-0.00868306\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 24.4974 | 0.879406 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 20.1051i | − 0.720803i | ||||||||
\(779\) | 32.1244 | 1.15097 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 21.3923 | 0.765477 | ||||||||
\(782\) | 6.92820i | 0.247752i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −16.4974 | −0.589194 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 48.0526i | − 1.71289i | −0.516239 | − | 0.856444i | \(-0.672668\pi\) | ||||
0.516239 | − | 0.856444i | \(-0.327332\pi\) | |||||||
\(788\) | − 20.2872i | − 0.722701i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 90.4974 | 3.21772 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 5.85641i | − 0.207967i | ||||||||
\(794\) | −10.5359 | −0.373905 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.92820 | 0.103787 | ||||||||
\(797\) | − 15.6077i | − 0.552853i | −0.961035 | − | 0.276426i | \(-0.910850\pi\) | ||||
0.961035 | − | 0.276426i | \(-0.0891502\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.8564 | −0.843979 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.2487i | 0.644384i | ||||||||
\(803\) | − 43.9090i | − 1.54951i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.21539 | −0.113257 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 6.74613i | − 0.237328i | ||||||||
\(809\) | −45.4449 | −1.59776 | −0.798878 | − | 0.601493i | \(-0.794573\pi\) | ||||
−0.798878 | + | 0.601493i | \(0.794573\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.4641 | −0.648362 | −0.324181 | − | 0.945995i | \(-0.605089\pi\) | ||||
−0.324181 | + | 0.945995i | \(0.605089\pi\) | |||||||
\(812\) | 22.1436i | 0.777088i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −11.4641 | −0.401817 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.875644i | 0.0306349i | ||||||||
\(818\) | 13.0718i | 0.457045i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.7321 | −1.31686 | −0.658429 | − | 0.752643i | \(-0.728779\pi\) | ||||
−0.658429 | + | 0.752643i | \(0.728779\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 3.85641i | − 0.134426i | −0.997739 | − | 0.0672129i | \(-0.978589\pi\) | ||||
0.997739 | − | 0.0672129i | \(-0.0214107\pi\) | |||||||
\(824\) | −1.35898 | −0.0473424 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 28.6410 | 0.996548 | ||||||||
\(827\) | − 11.6077i | − 0.403639i | −0.979423 | − | 0.201820i | \(-0.935315\pi\) | ||||
0.979423 | − | 0.201820i | \(-0.0646855\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.7846 | 0.826074 | 0.413037 | − | 0.910714i | \(-0.364468\pi\) | ||||
0.413037 | + | 0.910714i | \(0.364468\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.13844i | 0.108806i | ||||||||
\(833\) | 42.0526i | 1.45703i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 37.4641 | 1.29572 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 14.9282i | − 0.515686i | ||||||||
\(839\) | −33.1962 | −1.14606 | −0.573029 | − | 0.819535i | \(-0.694232\pi\) | ||||
−0.573029 | + | 0.819535i | \(0.694232\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.7846 | −0.647745 | ||||||||
\(842\) | 24.7321i | 0.852323i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12.9667 | −0.446331 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 103.426i | − 3.55375i | ||||||||
\(848\) | − 7.21539i | − 0.247778i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.46410 | 0.324425 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 10.4833i | − 0.358943i | −0.983763 | − | 0.179471i | \(-0.942561\pi\) | ||||
0.983763 | − | 0.179471i | \(-0.0574387\pi\) | |||||||
\(854\) | 13.8564 | 0.474156 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 21.6462 | 0.739851 | ||||||||
\(857\) | 44.4974i | 1.52000i | 0.649921 | + | 0.760002i | \(0.274802\pi\) | ||||
−0.649921 | + | 0.760002i | \(0.725198\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0000 | 0.375315 | 0.187658 | − | 0.982235i | \(-0.439910\pi\) | ||||
0.187658 | + | 0.982235i | \(0.439910\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 15.6218i | − 0.532080i | ||||||||
\(863\) | 23.1244i | 0.787162i | 0.919290 | + | 0.393581i | \(0.128764\pi\) | ||||
−0.919290 | + | 0.393581i | \(0.871236\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −25.9615 | −0.882209 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 20.7846i | 0.705476i | ||||||||
\(869\) | 88.6410 | 3.00694 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.07180 | 0.171851 | ||||||||
\(872\) | 15.3975i | 0.521424i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 11.3205 | 0.382922 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.4641i | 1.13000i | 0.825090 | + | 0.565001i | \(0.191124\pi\) | ||||
−0.825090 | + | 0.565001i | \(0.808876\pi\) | |||||||
\(878\) | − 3.94744i | − 0.133220i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.0526 | −1.58524 | −0.792620 | − | 0.609715i | \(-0.791284\pi\) | ||||
−0.792620 | + | 0.609715i | \(0.791284\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.1962i | 1.01618i | 0.861304 | + | 0.508091i | \(0.169649\pi\) | ||||
−0.861304 | + | 0.508091i | \(0.830351\pi\) | |||||||
\(884\) | −5.85641 | −0.196972 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.248711 | −0.00835562 | ||||||||
\(887\) | 33.8038i | 1.13502i | 0.823366 | + | 0.567511i | \(0.192094\pi\) | ||||
−0.823366 | + | 0.567511i | \(0.807906\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −69.0333 | −2.31530 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 24.5744i | − 0.822811i | ||||||||
\(893\) | 38.9808i | 1.30444i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 48.0000 | 1.60357 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 5.94744i | − 0.198469i | ||||||||
\(899\) | 9.58846 | 0.319793 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.3923 | −0.612737 | ||||||||
\(902\) | 30.1962i | 1.00542i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −48.4974 | −1.61300 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 30.0000i | − 0.996134i | −0.867139 | − | 0.498067i | \(-0.834043\pi\) | ||||
0.867139 | − | 0.498067i | \(-0.165957\pi\) | |||||||
\(908\) | − 26.4308i | − 0.877136i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.5885 | 0.781520 | 0.390760 | − | 0.920493i | \(-0.372212\pi\) | ||||
0.390760 | + | 0.920493i | \(0.372212\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.5885i | 0.416617i | ||||||||
\(914\) | −2.00000 | −0.0661541 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.5692 | 0.580503 | ||||||||
\(917\) | − 73.7654i | − 2.43595i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.9615 | 1.87899 | 0.939494 | − | 0.342566i | \(-0.111296\pi\) | ||||
0.939494 | + | 0.342566i | \(0.111296\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 27.1244i | − 0.893293i | ||||||||
\(923\) | 5.46410i | 0.179853i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −7.60770 | −0.250004 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 18.7180i | − 0.614447i | ||||||||
\(929\) | 44.3731 | 1.45583 | 0.727917 | − | 0.685666i | \(-0.240489\pi\) | ||||
0.727917 | + | 0.685666i | \(0.240489\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 68.7128 | 2.25197 | ||||||||
\(932\) | 41.0718i | 1.34535i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −27.3590 | −0.895213 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 4.14359i | − 0.135365i | −0.997707 | − | 0.0676827i | \(-0.978439\pi\) | ||||
0.997707 | − | 0.0676827i | \(-0.0215605\pi\) | |||||||
\(938\) | 12.0000i | 0.391814i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.1769 | 1.14673 | 0.573367 | − | 0.819298i | \(-0.305637\pi\) | ||||
0.573367 | + | 0.819298i | \(0.305637\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 24.9282i | − 0.811774i | ||||||||
\(944\) | 8.86156 | 0.288419 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.823085 | −0.0267608 | ||||||||
\(947\) | − 57.7128i | − 1.87541i | −0.347427 | − | 0.937707i | \(-0.612944\pi\) | ||||
0.347427 | − | 0.937707i | \(-0.387056\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.2154 | 0.364067 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 32.7846i | − 1.06256i | ||||||||
\(953\) | − 36.3923i | − 1.17886i | −0.807819 | − | 0.589431i | \(-0.799352\pi\) | ||||
0.807819 | − | 0.589431i | \(-0.200648\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.784610 | 0.0253761 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.69358i | 0.280877i | ||||||||
\(959\) | 12.0000 | 0.387500 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | − 2.92820i | − 0.0944091i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −23.8949 | −0.769602 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 25.8038i | − 0.829796i | −0.909868 | − | 0.414898i | \(-0.863817\pi\) | ||||
0.909868 | − | 0.414898i | \(-0.136183\pi\) | |||||||
\(968\) | 55.4256i | 1.78145i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.4449 | 0.559832 | 0.279916 | − | 0.960024i | \(-0.409693\pi\) | ||||
0.279916 | + | 0.960024i | \(0.409693\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.87564i | 0.0921889i | ||||||||
\(974\) | −17.8564 | −0.572156 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.28719 | 0.137230 | ||||||||
\(977\) | 5.46410i | 0.174812i | 0.996173 | + | 0.0874060i | \(0.0278578\pi\) | ||||
−0.996173 | + | 0.0874060i | \(0.972142\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 29.7846 | 0.951920 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 10.1577i | − 0.324144i | ||||||||
\(983\) | − 48.5885i | − 1.54973i | −0.632126 | − | 0.774866i | \(-0.717818\pi\) | ||||
0.632126 | − | 0.774866i | \(-0.282182\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −6.39230 | −0.203572 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.56922i | 0.304437i | ||||||||
\(989\) | 0.679492 | 0.0216066 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.8564 | 0.980186 | 0.490093 | − | 0.871670i | \(-0.336963\pi\) | ||||
0.490093 | + | 0.871670i | \(0.336963\pi\) | |||||||
\(992\) | − 17.5692i | − 0.557823i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.9282 | −0.410058 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.5167i | 0.808121i | 0.914732 | + | 0.404060i | \(0.132401\pi\) | ||||
−0.914732 | + | 0.404060i | \(0.867599\pi\) | |||||||
\(998\) | − 17.8038i | − 0.563571i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2025.2.b.g.649.3 | 4 | ||
3.2 | odd | 2 | 2025.2.b.h.649.2 | 4 | |||
5.2 | odd | 4 | 2025.2.a.m.1.1 | 2 | |||
5.3 | odd | 4 | 405.2.a.g.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 2025.2.b.g.649.2 | 4 | ||
15.2 | even | 4 | 2025.2.a.g.1.2 | 2 | |||
15.8 | even | 4 | 405.2.a.h.1.1 | yes | 2 | ||
15.14 | odd | 2 | 2025.2.b.h.649.3 | 4 | |||
20.3 | even | 4 | 6480.2.a.br.1.2 | 2 | |||
45.13 | odd | 12 | 405.2.e.l.136.1 | 4 | |||
45.23 | even | 12 | 405.2.e.i.136.2 | 4 | |||
45.38 | even | 12 | 405.2.e.i.271.2 | 4 | |||
45.43 | odd | 12 | 405.2.e.l.271.1 | 4 | |||
60.23 | odd | 4 | 6480.2.a.bi.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.2.a.g.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
405.2.a.h.1.1 | yes | 2 | 15.8 | even | 4 | ||
405.2.e.i.136.2 | 4 | 45.23 | even | 12 | |||
405.2.e.i.271.2 | 4 | 45.38 | even | 12 | |||
405.2.e.l.136.1 | 4 | 45.13 | odd | 12 | |||
405.2.e.l.271.1 | 4 | 45.43 | odd | 12 | |||
2025.2.a.g.1.2 | 2 | 15.2 | even | 4 | |||
2025.2.a.m.1.1 | 2 | 5.2 | odd | 4 | |||
2025.2.b.g.649.2 | 4 | 5.4 | even | 2 | inner | ||
2025.2.b.g.649.3 | 4 | 1.1 | even | 1 | trivial | ||
2025.2.b.h.649.2 | 4 | 3.2 | odd | 2 | |||
2025.2.b.h.649.3 | 4 | 15.14 | odd | 2 | |||
6480.2.a.bi.1.2 | 2 | 60.23 | odd | 4 | |||
6480.2.a.br.1.2 | 2 | 20.3 | even | 4 |